PorcoRosso-
It's not the *range* of V1 that allows the t/o, it's the t/o *weight* that allows the takeoff. Unless your carrier allows a range of V speeds from which to choose (a few do, but that's the subject for another thread), then the V1 for a given weight will be the same for a 6000' runway as a 12,000' runway.
------------------